Distributed Indeterminacy Form

Florentin Smarandache

Distributed Indeterminacy Form

To Selcuk Topal "I can see that people use indeterminacy in a wrong way. " — No, "Indeterminacy" is used correctly, it is a generic (general) name to mean everything in between the opposites.

In neutrosophy we have: the opposites <A> and <antiA>, while in between them is <neutA>.

Therefore, Indeterminacy = <neutA>.

Please do not take 'ad literam' (literally) the word "indeterminacy" only as something not clear, etc. [as in a language dictionary].

For example, in games "indeterminacy" means "tie game" (neither winning, nor losing).

In physics, for charged particles, you have: positive particle, negative particle, and neutral particle (no charge); hence "Indeterminacy" = "neutral particle".

In decision making "indeterminacy: means "pending" (neither taking a decision, nor rejecting a decision). Again, please do not make the confusion considering "Indeterminacy" as the narrow sense definition from a language dictionary. — About the neutrosophic score, accuracy, and certainty functions, they are clearly defined and motivated: score function = the average of positiveness; accuracy function = the difference between positiveness and negativeness; certainty function = positiveness.

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Nidus Idearum. Scilogs, VIII: painting by numbers

They all determine a total ordering on the set of triplets (T, I, F).

You have first to use the score function, then if you get equality, use the accuracy function, and if you get again equality you use certainty function; now if you still get equality, the two triplets are equal. "The indeterminacy factor is dependent on truth and falsity values". — This is false in general, since indeterminacy is INDEPENDENT of truth and falsehood, and this was the main distinction between neutrosophic set and other types of sets.

But there are cases when indeterminacy is partially dependent, or totally dependent of T and F, depending on the application and on the experts: http://fs.unm.edu/Indeterminacy.pdf. "We propose to distribute the indeterminacy on truth and falsity to be aligned with real life applications"; (T, I, F) is reduced to ( T – TI, 0, F – FI )." — This transformation produces a suboptimal result (T – TI, 0, F – FI), which is not equivalent with (T, I, F). This transformation does not work if your application has a middle (neutral) term. a) For example, if your application is about a soccer game, and if you distribute the indeterminacy, you LOSE information, you lose the possibility of saying something about a "tie game" (i.e. you eliminate the degree of "tie game", so your work is incomplete, you give the degree of winning and the degree of defeated, but you say nothing on the degree of tie game).